We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations of Scott-Blair elements to construct a series of well-known fractional linear viscoelastic models, such as Kelvin-Voigt, Maxwell, Kelvin-Zener and Poynting-Thomson. We also consider a fractional quasi-linear version of Fung's model to account for stress/strain nonlinearity. The fractional viscoelastic models are combined with a fractional visco-plastic device, coupled with fractional viscoelastic models involving serial combinations of Scott-Blair elements. We then develop a general return-mapping procedure, which is fully implicit for linear viscoelastic models, and semi-implicit for the quasi-linear case. We find that, in the correction phase, the discrete stress projection and plastic slip have the same form for all the considered models, although with different property and time-step dependent projection terms. A series of numerical experiments is carried out with analytical and reference solutions to demonstrate the convergence and computational cost of the proposed framework, which is shown to be at least first-order accurate for general loading conditions. Our numerical results demonstrate that the developed framework is more flexible, preserves the numerical accuracy of existing approaches while being more computationally tractable in the visco-plastic range due to a reduction of 50% in CPU time. Our formulation is especially suited for emerging applications of fractional calculus in bio-tissues that present the hallmark of multiple viscoelastic power-laws coupled with visco-plasticity.

Dopaminergic treatment (DT), the standard therapy for Parkinson's disease (PD), alters the dynamics of functional brain networks at specific time scales. Here, we explore the scale-free functional connectivity (FC) in the PD population and how it is affected by DT. We analyzed the electroencephalogram of: (i) 15 PD patients during DT (ON) and after DT washout (OFF) and (ii) 16 healthy control individuals (HC). We estimated FC using bivariate focus-based multifractal analysis, which evaluated the long-term memory and multifractal strength of the connections. Subsequent analysis yielded network metrics (node degree, clustering coefficient and path length) based on FC estimated by or . Cognitive performance was assessed by the Mini Mental State Examination (MMSE) and the North American Adult Reading Test (NAART). The node degrees of the networks were significantly higher in ON, compared to OFF and HC, while clustering coefficient and path length significantly decreased. No alterations were observed in the networks. Significant positive correlations were also found between the metrics of networks and NAART scores in the HC group. These results demonstrate that DT alters the multifractal coupled dynamics in the brain, warranting the investigation of scale-free FC in clinical and pharmacological studies.

An investigation of transient second sound phenomena due to moving heat sources on planar random media is conducted. The spatial material randomness of the relaxation time is modeled by Cauchy or Dagum random fields allowing for decoupling of fractal and Hurst effects. The Maxwell-Cattaneo model is solved by a second-order central differencing. The resulting stochastic fluctuations of Mach wedges are examined and compared to unperturbed Mach wedges resulting from the heat source traveling in a homogeneous domain. All the examined cases are illustrated by simulation movies linked to this paper.